Tag: Bifurcation

Free Download Economic Bifurcation And Chaos
English | 2025 | ISBN: 9811293651 | 715 Pages | PDF (True) | 18 MB
Economic Bifurcation and Chaos provides a unified presentation of the contributions to the literature on economic bifurcation, nonlinear dynamics, and chaos by William A Barnett and his coauthors. The span of the research begins in 1988 with Barnett’s initial finding of chaos in economic data. The book continues with subsequent findings of bifurcation in all dynamical macroeconomic models so far tested by Barnett and his coauthors. The research covered extends over 3 decades to his recent findings of Shilnikov chaos in New Keynesian models of the UK and US economies. While methodology for testing for bifurcation, nonlinear dynamics, and chaos are fundamental to the research, the book’s ultimate objectives focus on implications for robustness of dynamical inferences and implications for policy.

Free Download Yuri A. Kuznetsov, Hil G. E. Meijer, "Numerical Bifurcation Analysis of Maps: From Theory to Software"
English | 2019 | pages: 424 | ISBN: 1108499678 | PDF | 8,4 mb
This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB® software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze more complicated models from modern engineering, ecology, and economics.

Free Download Bifurcation, Symmetry and Patterns by Jorge Buescu, Sofia B. S. D. Castro, Ana Paula Silva Dias, Isabel Salgado Labouriau
English | PDF | 2003 | 215 Pages | ISBN : 3764370203 | 20 MB
This book represents the latest developments on both the theory and applications of bifurcations with symmetry. It includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern mathematics at the same time as it contains work of young mathematicians in new directions. The range of topics includes mathematical biology, pattern formation, ergodic theory, normal forms, one-dimensional dynamics and symmetric dynamics.

Free Download Bifurcation and Chaos: Theory and Applications by Jan Awrejcewicz
English | PDF | 1995 | 281 Pages | ISBN : 3642793312 | 24.5 MB
Bifurcation and Chaos presents a collection of especially written articles describing the theory and application of nonlinear dynamics to a wide variety of problems encountered in physics and engineering. Each chapter is self-contained and includes an elementary introduction, an exposition of the present state of the art, and details of recent theoretical, computational and experimental results. Included among the practical systems analysed are: hysteretic circuits, Josephson circuits, magnetic systems, railway dynamics, rotor dynamics and nonlinear dynamics of speech. This book contains important information and ideas for all mathematicians, physicists and engineers whose work in R & D or academia involves the practical consequences of chaotic dynamics.